Power amplifiers 1508 are an important component in many wireless communication systems 1500, but they often introduce non-linearity. Digital pre-distortion (DPD) is a technique used to linearize a power amplifier 1508 in a transmitter to improve the efficiency of the power amplifier 1508. A digital pre-distortion circuit 1504 inversely models the gain and phase characteristics of the power amplifier 1508 and, when combined with the amplifier 1508, produces an overall system that is more linear and reduces distortion than would otherwise be caused by the power amplifier 1508. An inverse distortion is introduced into the input 1506 of the amplifier 1508, thereby reducing any non-linearity that the amplifier 1508 might otherwise exhibit. When developing an effective DPD 1504, it is often challenging to capture the nonlinear distortion and memory effects of the power amplifier 1508 using an accurate behavioral model.
Volterra series have been used to model the non-linear behavior of a non-linear system, such as a DPD system 1504 or a power amplifier 1508. Among other benefits, a Volterra series can capture the memory effects of the modeled non-linear system. The Volterra series can be used to approximate the response of a non-linear system to a given input 1502 when the output 1510 of the non-linear system depends on the input to the system at various times. Volterra series are thus used to model non-linear distortion in a wide range of devices including power amplifiers 1508.
Due to the complexity of a Volterra series, however, such as a large number of coefficients, the Volterra series is often modeled using a generalized memory polynomial (GMP) model, which reduces complexity by pruning the Volterra series to a reduced number of terms. Thus, GMP is a simplification of an ideal Volterra series. Pruning of terms can result in loss of performance in some cases. A need remains for improved techniques for modeling a target Volterra series.